Quantum Reality Filters

An anhomomorphic logic \ascript ^* is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" \phi_a\in\ascript ^* for the system. Reality filters are employed to eliminate unwanted potential realities until only $\phi_a$ remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure $\mu$ can generate or actualize a \phi\in\ascript ^* if $\mu (A)$ is a quantum integral with respect to $\phi$ for a density function $f$ over events $A$. In this sense, $\mu$ is an "average" of the truth values of $\phi$ with weights given by $f$. We mainly discuss relations between these filters and their existence and uniqueness properties. For example, we show that a quadratic reality generated by a quantum measure is unique. In this case we obtain the unique actual quadratic reality.Comment: 25 page

Hilbert Spaces from Path Integrals

It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics.Comment: 22 pages. Minor updates to match published versio

A Bell Inequality Analog in Quantum Measure Theory

One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as ``screening off''. We show that if one assumes, more generally, a joint {\it quantal measure}, or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of $\sqrt{2}$. The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a {\it question}: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the {\it observation} that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledgements, now closer to published versio

Dynamics & Predictions in the Co-Event Interpretation

Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events for a range of systems including single time 'Copenhagen measurements'. This 'co-event interpretation' presents us with a new ontology, in which a single 'co-event' is real. A new ontology necessitates a review of the dynamical & predictive mechanism of a theory, and in this paper we begin the process by exploring means of expressing the dynamical and predictive content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein

Twistor form of massive 6D superparticle

The massive six-dimensional (6D) superparticle with manifest (n, 0) supersymmetry is shown to have a supertwistor formulation in which its “hidden” (0, n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin; for n = 1 it propagates the 6D Proca supermultiplet.PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society.This is the final version of the article. It was first available from IOP Science via http://dx.doi.org/10.1088/1751-8113/49/2/02540

Carbon Nanotubes: Artificial Nanomaterials to Engineer Single Neurons and Neuronal Networks

Carbon nanotubes are increasingly employed in basic neuroscience approaches, and they have been used in the design of neuronal interfaces or in that of scaffolds promoting neuronal growth in vitro. Ultimately, carbon nanotubes are thought to hold the potential for the development of innovative neurological implants. In this framework, it is particularly relevant to document the impact of interfacing such materials with nerve cells. Carbon nanotubes were shown, when modified with biologically active compounds or functionalized in order to alter their charge, to affect neurite outgrowth and branching. Notably, purified carbon nanotubes used as scaffolds can promote the formation of nanotube 12neuron hybrid networks, able per se to affect neuron integrative abilities, network connectivity, and synaptic plasticity. We focus this review on our work over several years directed to investigate the ability of carbon nanotube platforms in providing a new tool for non genetic manipulations of neuronal performance and network signaling. \ua9 2012 American Chemical Society